Spectra of the excited giant gravitons from the two loop dilatation operator
Date
2016-09-19
Authors
Ali, Abdelhamid Mohamed Adam
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Abstract
The AdS/CFT correspondence is a conjectured exact duality between type IIB string theory on the
AdS5 S5 background and N = 4 Super Yang-Mills theory, a conformal eld theory (CFT), on
the boundary of the AdS space. A speci c observable of the CFT, which can be read from the two
point correlation function, is the anomalous dimension. In this dissertation we will compute spectra of
anomalous dimensions of excited giant gravitons up to two loops in a speci c limit. We are interested
in the anomalous dimensions because the AdS/CFT correspondence associates them with energies of
states in quantum gravity. We study operators constructed using n Z elds and m Y elds with
n << m: In this case m
n is a small parameter. At the leading order in m
n and at large N, the problem of
determining the anomalous dimensions can be mapped into the dynamics of m non-interacting magnons.
The subleading terms at two loops, computed for the rst time in this dissertation, induce interactions
between the magnons. Even after including this new correction, we nd the BPS operators remain BPS.
Description
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 2016.